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Introduction to Probability

George G. Roussas
Academic Press
Publication Date: 
Number of Pages: 
[Reviewed by
Robert W. Hayden
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Here we have a very traditional mathematics text on the topic of probability. Readers should be comfortable with multiple integrals and, in spots, a little linear algebra. The writing is clear and concise. The presentation style is theorem, proof, example, exercise. Most of the latter ask the student to “show” or “derive”. The first chapter (five pages) gives some sketches of applications. Later “applications” are even briefer and appear fictional and only suggestive. There is no mention of computers. Fairly detailed solutions to the even-numbered exercises may be found at the back of the book. A final chapter sketches some applications to statistics but here too there is little contact with reality, combined with poor advice on how to apply the material.

The book has no outstanding vices or virtues as a text in mathematical probability for mathematics majors. It would probably not be suitable if a significant number of the students are primarily interested in applications.

After a few years in industry, Robert W. Hayden ( taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.

1. Some Motivating Examples
2. Some Fundamental Concepts
3. The Concept of Probability and Basic Results
4. Conditional Probability and Independence
5. Numerical Characteristics of a Random Variable
6. Some Special Distributions
7. Joint Probability Density Function of Two Random Variables and Related Quantities
8. Joint Moment Generating Function, Covariance and Correlation Coefficient of Two Random Variables
9. Some Generalizations to k Random Variables, and Three Multivariate Distributions
10. Independence of Random Variables and Some Applications
11. Transformation of Random Variables
12. Two Modes of Convergence, the Weak Law of Large Numbers, the Central Limit Theorem, and Further Results
13. An Overview of Statistical Inference
Some Notation and Abbreviations
Answers to the Even-numbered Exercises